You need to look at the numbers when you're ready to transact. What your crossover is worth now, what the truck will lease for then, what financing deals may or may not be available will all change.
I'm not sure why you've already decided you will lease the truck, perhaps you're planning to take advantage of some kind of business write off. I would personally never put anything down on a lease, though I have argued with people on here about that particular decision. The reality is you need to look at the numbers. Some banks will adjust the interest you pay on your lease to account for your down payment, some don't.
Consider a $9,000 lease, $250 per month for 36 months. Consider you pay $1,000 up front as a down payment.
Example 1: $1,000 lowers the amount due on the lease to $8,000 lowering your monthly payment to $222.22 from $250, the downpayment has accomplished nothing. Over the 36 months you will have still paid the same $9,000.
Example 2: $1,000 up front changes the amount owed and other fees generally applicable to a lease (gap insurance etc) and your payment drops to $215, your total over the lease is now $8,740 ($1,000 down and $7,740 in payments).
You need to look at the numbers. In general if you know you will be purchasing the truck at the end of the lease it's more financially advantageous to just purchase it from the start.